In this presentation I will expose our recent results on the Restricted Boltzman Machine (RBM). The RBM is a generative model very similar to the Ising model, it is composed of both visible and hidden binary variables, and traditionally used in the context of machine learning. In this context, the goal is to infer the parameters of the RBM such that it reproduces correctly a dataset’s distribution. Although they have been widely used in computer science, the phase
diagram of this model is not known precisely in the context of learning. In particular, it is not known how the parameters influence the learning, and what exactly is learned within the parameters of the model. After an introduction to some aspects of Machine learning, I will expose our work, showing how the SVD of the data governs the first phase of the learning and how this decomposition helps to understand the dynamics and the equilibrium properties of the model.
Réf:
Aurélien Decelle, Giancarlo Fissore and Cyril Furtlehner, Spectral dynamics of learning in restricted Boltzmann machines, EuroPhys. Lett. 119, 60001 (2017)
Aurélien Decelle, Giancarlo Fissore and Cyril Furtlehner, Thermodynamics of Restricted Boltzmann Machines and related learning dynamics, preprint cond-mat arXiv:1803.01960 (2018).